I was trying to find out what the mechanisms are behind urgency, frequency etc are and one paper I was just reading may have some relevance here. Apparently in active colitis transit time in the proximal colon (right side) is slowed and constipation can result there even though there will still be liquid stools. This may be what can cause pain in the right side and in the short term a laxative might give relief until it can be investigated.
https://www.tandfonline.com/doi/abs/10.3109/00365529009091905?journalcode=igas20